If A = {x ∈ Z | x² ≤ 4}, how many proper subsets does A have?
Advertisement
Answer and explanation
Correct answer: 31
For integer x, the inequality x² ≤ 4 gives −2 ≤ x ≤ 2. Hence A = {−2, −1, 0, 1, 2}, which has five elements. A set with n elements has 2^n total subsets, so A has 2^5 = 32 subsets. A proper subset is any subset other than the set itself, so the number of proper subsets is 32 − 1 = 31. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
For integer x, the inequality x² ≤ 4 gives −2 ≤ x ≤ 2. Hence A = {−2, −1, 0, 1, 2}, which has five elements. A set with n elements has 2^n total subsets, so A has 2^5 = 32 subsets. A proper subset is any subset other than the set itself, so the number of proper subsets is 32 − 1 = 31. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement